It's an old joke among real estate professionals: the price of a house depends on three factors—location, location, and location. A half-million dollars will buy a sprawling estate in Wichita but only a modest apartment in New York. Economists have long suspected that geographic space limitations have a lot to do with this discrepancy. The logic goes that houses are cheap in Wichita because there is plenty of surrounding space on which to build new homes, but Manhattan Island isn't getting any larger. Unfortunately, it has been difficult to precisely quantify the importance of space limitations in housing prices, due to data limitations as well as a large number of potentially confounding factors that also matter for housing markets.

An exciting new paper by Albert Saiz of the University of Pennsylvania's Wharton School makes a significant advance in this area by using detailed geographic data to show how both space limitations and local development policies affect housing prices. This paper will be a big help to those who study the geographic pattern of urban development in the United States. It will also be widely cited in future studies of local development policy. But, as we argue below, one must be careful when using the Saiz results to infer anything about the rise-and-fall in housing prices during the recent housing bubble.

The main empirical contribution of the Saiz paper is to calculate, for each major city, the amount of land that cannot be used to build houses because of geographical constraints. Lying next to a major body of water such as an ocean or one of the Great Lakes clearly limits a city's ability to build, and figuring out which cities are affected is trivial. In fact, a "coastal dummy variable" has long been used in models of housing prices. But new construction can also be limited by inland waterways, such as wetlands or lakes. It is also tough to build on steeply sloped terrain, as in the foothills of mountains. To measure the importance of these latter two factors on a city-by-city basis, Saiz uses Geographic Information System (GIS) techniques and highly detailed topographical data from the United States Geological Survey. Specifically, for all the land within 50 kilometers of each large city's center, Saiz measures the geographic characteristics of finely disaggregated parcels (for example, 30-meter-by-30-meter squares). He then adds up the prevalence of water or steep slopes across individual parcels to get overall, city-specific measures of geographically determined space constraints. According to this method, the most constrained city in the country is Ventura (CA), where almost 80 percent of the land within 50 kilometers of the city center is undevelopable. Miami, Fort Lauderdale, and New Orleans are close behind, with about 75 percent of their land essentially off limits to residential construction. At the other end of the spectrum lie cities like Wichita (KS), Indianapolis (IN), Dayton-Springfield (OH), and McAllen-Edinburg-Mission (TX), where less than 2 percent of the land is undevelopable.

Saiz then confronts his city-specific measure of space constraints with the data. He finds that the fraction of undevelopable land is correlated with house price levels, house price growth from 1970 to 2000, average income levels, the extent of tourism, and a measure of creativity (measured by the number patents awarded to residents of the city). The index is not correlated with the size of cities, or with the share of city residents who have a bachelor's degree or work in manufacturing. Many of these correlations are consistent with the detailed theoretical model that Saiz builds to explain how space constraints should matter for a number of city-specific variables. 1

A question that Saiz explores in depth is how space constraints matter for the way a city adjusts to a positive demand shock, which causes more people to want to live in that city. Cities that are space-constrained have a tough time accommodating a positive shock with a burst of new construction. In formal terms, the supply curve for new homes in space-constrained cities will be inelastic, or close to vertical. As a result, a positive shift in housing demand will result mostly in higher housing prices, not more construction.

These predictions are borne out by the data. Using regression models, Saiz finds that local supply elasticities are determined both by his space-constraint measure and by an index of local building regulations, which was also developed at Wharton.2 Interestingly, the local-regulation index is itself strongly correlated with Saiz's space-constraint index, as space-constrained cities tend to have stricter regulatory limits on new construction. This correlation provides compelling evidence for something that many housing economists have long suspected—local voters seek to protect the values of expensive homes by preventing new homes from being built.3 This finding may be puzzling to some, as it may be hard to imagine why land-constrained cities would need to implement further restrictions on new construction. However, some new development, perhaps via dense apartment buildings, is usually possible. Note that unlike a lot of correlations in economics, we can be reasonably sure that the direction of causality runs from space constraints to local regulations, not the other way around. After all, it is hard to create a new mountain, lake, or ocean through the political process.

The Saiz paper is forthcoming in a top economics journal, and its results are already being used by housing economists. We draw from it ourselves in a paper that investigates why so many economists missed the housing bubble.4 But we caution that one should not push the Saiz results too far. The Saiz paper concerns the slopes of housing supply curves in different cities. As a result, it says nothing about shifts in housing demand that might have occurred during the housing boom. For example, the Saiz results would predict that, during the housing boom, prices in high-supply-elasticity cities like Wichita would rise less than prices in low-elasticity cities like Boston. Sure enough, this is what we find in the data. However, this finding does not prove that the boom was caused by some uniform, nationwide increase in housing demand (arising, for example, from easier subprime lending, or from lower interest rates). It is true we would expect a uniform demand increase to have a small effect on Wichita's prices and a big effect on Boston's prices. But because Wichita has a flat supply curve, its house prices will be stable no matter what happens to demand there. To determine whether Wichita and Boston saw similar increases in demand, one would have to look not only at prices but also at quantities (that is, new construction). Researchers should therefore be careful when using the Saiz results to study the housing boom—a point we hope to revisit in future posts.

By Chris Foote, senior economist and policy adviser at the Boston Fed (with Atlanta Fed economist Kris Gerardi and Boston Fed economist Paul Willen)


1 We will refer interested readers to the paper for the model's details, but it assumes that people can move freely between cities, so that the utility of people is equalized across cities. The model also assumes all the jobs in a city are located in a central business district, to which each city resident must commute.

2 Specifically, to measure the extent of land-use restrictions in a metropolitan area, Saiz uses the Wharton Residential Urban Land Regulation Index (WRI) that was created by Gyourko, Saiz, and Summers (2007).

3 Because the land-regulation index is endogenous, Saiz also provides some instrumental variables (IV) regressions that depend on city-level variation in general political attitudes toward regulation to identify the specific effect of housing regulations on housing-supply elasticities. The IV results are also consistent with a role for both space constraints and regulations in determining housing-supply elasticities.

4 Specifically, we show that housing prices rose in places like Phoenix and Las Vegas, which, according to the Saiz results, should have had very elastic housing prices (flat supply curves). Thus, we argue that some other factor besides building constraints must be invoked to explain the rapid run-up in prices for cities like these.